1) John-Nirenberg estimate
John-Nirenberg估计
1.
The main aim of this thesis is to study the properties of the maps for Heisenberg group target, which include Lipschitz and Holder continuity, L~(P)(#,H~(n)) , W~(1,p)(#,H~(n)) , BMO and John-Nirenberg estimates, embedded theorems, Poincare inequalities and reverse Poincare inequalities, the regul-arities about the minimizers.
本文的主要目的是系统研究靶流形为Heisenberg群的函数及其空间的性质,其中包括Lipschitz及Hlder连续性、空间L~p(Ω,H~n)及W~(1,p)(Ω,H~n)的性质、空间BMO(Ω,H~n)的性质及其上的John-Nirenberg估计、嵌入定理、Poincare不等式和逆Poincare不等式、能量极小映射的存在性、正则性及用调和函数逼近能量极小映射等问题。
2) John-Nirenberg inequality
John-Nirenberg不等式
1.
A John-Nirenberg inequality is proved for Lipschitz functions on R~n.
本文证明了R~n上Lipschitz函数空间的John-Nirenberg不等式,由此得到了Lipschitz函数空间的一些新的范数等价刻划。
3) John-Nirenberg type inequality
John-Nirenberg型不等式
4) John domain
John域
1.
The main purpose of this paper is to study the relation among a John domain,a uniform domain and a linearly locally connected domain.
本文研究了∫ΩBn中的John域与一致域和线性局部连通域的关系。
2.
In this paper, the authors prove that f is a quasiconformal mapping if and only if f(D) is a John domain for any John domain D in Rn.
设f:Rn→Rn是一同胚,该文证明了f是拟共形映射的充要条件是f将Rn中的任-John域映成Rn中的John域。
3.
In this paper,we prove that a bounded uniform domain must be a John domain and John domains are in- variant under quasiconformal mappings.
本文证明了有界一致域必定是John域和John域的拟共不变性。
5) John disk
John圆
1.
In this paper,we prove that D is a b-John disk if and only if there exists a constant c≥1 such that k_D(x_1,x_2)≤cH_D(x_1,x_2) for all x_1,x_2∈D.
设D是R~2中的Jordan域,本文证明了D是b-John圆当且仅当存在常数c≥1,对任意的x_1,x_2∈D,有k_D(x_1,x_2)≤cH_D(x_1,x_2),这里kD(x_1,x_2)表示D中x_1与x_2二点的拟双曲距离,H_D(x_1,x_2)=1/2log(1+(l(γ))/(d(x_1,■D)))(1+(l(γ))/(d(x_2,■D))),其中l(γ)为D中连结x_1与x_2二点的拟双曲测地线的欧几里德长度。
2.
We proved that DR is a John disk if and only if D has the John decomposable property,and that DR is a quasidisk if and only if for any z1,z2∈D,there exists a constant c≥1,such that 1cλD(z1,z2)≤λD*(z1,z2)≤cλD(z1,z2).
证明D-R2是John圆当且仅当D具有John可分解性质;D-R2是拟圆当且仅当对于任意的z1,z2∈D,存在常数c≥1,使得1cλD(z1,z2)≤λD*(z1,z2)≤cλD(z1,z2)。
3.
The main aim of this dissertation is to discuss some problems of quasiconformalmappings with respect to quasidisks, John disks and the Apollonian metric.
本文主要研究拟共形映射与拟圆、John圆和Apollon度量的相关问题。
6) Nirenberg inequality
Nirenberg不等式
补充资料:John lewis
john lewis
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